The Time War, was said to have been about The Time Lords and The Daleks going back into each other's pasts, and "turning the other side's wins into losses". This is exactly what The Great Intelligence did by going into The Doctor's Time Stream, and Clara fought back reversing those losses.

So, really, we kinda saw a Time War play out in The Name of The Doctor. So, this really may play into being a hint the HurtDoctor is indeed a product of The Time War